Wednesday, July 29, 2015

If quantum computing is at the Goddard level that would be a good thing for quantum computing. This means that the major fundamental breakthrough that would put them over the top was in hand and merely a lot of investment, engineering and scaling was needed. The goal of being able to solve NP-hard or NP-Complete problems with quantum computers is similar to being able to travel to the moon, mars or deeper into space with rockets. Conventional flight could not achieve those goals because of the lack of atmosphere in space. Current computing seems like they are very limited in being able to tackle NP-hard and NP Complete problems. Although clever work in advanced mathematics and approximations can give answers that are close on a case by case basis.

Dream on.

Three comments were actually sensible:

Quantum computers cannot solve NP-Hard or NP-Complete problems -- at least, no faster than a classical computer. This is one of the most basic results in the field, and the author keeps on making hash of it. This article should not be taken seriously if it's rife with such basic errors.

[Goddard's rockets were] Designed on totally incorrect physics. The true revolutionaries of rocket propulsion all have German last names.

Quantum computing is about where teleportation, strong AI, a perfect cure for cancer, etc. is, namely it is completely unclear whether it will ever work. All this bullshit about Quantum Computing is just that: Bullshit. We do not even know whether the physics allows it, all we know is that the current theory (which we know is incomplete and inaccurate) would allow it if it was accurate.

[1920 editorial] That Professor Goddard, with his "chair" in Clark College and the countenancing of the Smithsonian Institution, does not know the relation of action and reaction, and of the need to have something better than a vacuum against which to react — to say that would be absurd. Of course he only seems to lack the knowledge ladled out daily in high schools.

[1969 ocrrection] Further investigation and experimentation have confirmed the findings of Isaac Newton in the 17th Century and it is now definitely established that a rocket can function in a vacuum as well as in an atmosphere. The Times regrets the error.[

Goddard really did get his Newtonian physics wrong, but the NY Times editorial did not correctly state the error. He needed something better than a vacuum to stabilize the rocket.

As far as I know, no publication has similarly denounced quantum computing. Dark Buzz fills the gap.

Monday, July 27, 2015

Deepak Chopra, M.D.: “For a century, science has invalidated ‘soft’ questions about truth, beauty, and transcendence. It took considerable courage therefore for Frank Wilczek to declare that such questions are within the framework of ‘hard’ science. Anyone who wants to see how science and transcendence can be compatible must read this book. Wilczek has caught the winds of change, and his thinking breaks through some sacred boundaries with curiosity, insight, and intellectual power.”

There is a fine line between the frontiers of hard physics and crackpot babble, I guess.

The neutron–proton mass difference, one of the most consequential parameters of physics, has now been calculated from fundamental theories. This landmark calculation portends revolutionary progress in nuclear physics.

The article is behind a paywall, so I cannot assess how revolutionary it is. My guess is that it uses the masses of the protons and neutrons to estimate the masses of the up and down quarks, and then uses the quark masses to calculate the proton and neutron masses. It does not sound revolutionary to me.

If Ptolemy’s epicycles worked, would we consider them to be beautiful?

Ptolemy’s epicycles did work. I scratch my head at how scientists can get this so wrong.

In Ptolemy's Almagest, the principal epicycles were just his way of representing the orbit of the Earth. The orbits of Earth and Mars could be approximated by circles, and the view of Mars from Earth can be represented by the vector difference of those two circles. The Earth circle was called an epicycle. There were also minor epicycles to correct for the orbits not being exactly circular.

So yes, epicycles did work to approximate the orbits, and the same main idea is used today whenever anyone describes a planetary orbit, as viewed from the Earth.

Saturday, July 25, 2015

The NY Times has a profile of a mathematician, so of course it has to explain whether he has won a Nobel Prize and whether he is crazy like all the other mathematicians:

He has since won many other prizes, including a MacArthur ‘‘genius’’ grant and the Fields Medal, considered the Nobel Prize for mathematicians. Today, many regard Tao as the finest mathematician of his generation. ...

Possibly the greatest mathematician since antiquity was Carl Friedrich Gauss, a dour German born in the late 18th century. He did not get along with his own children and kept important results to himself, seeing them as unsuitable for public view. They were discovered among his papers after his death. Before and since, the annals of the field have teemed with variations on this misfit theme, from Isaac Newton, the loner with a savage temper; to John Nash, the ‘‘beautiful mind’’ whose work shaped economics and even political science, but who was racked by paranoid delusions; to, more recently, ­Grigory Perelman, the Russian who conquered the Poincaré conjecture alone, then refused the Fields Medal, and who also allowed his fingernails to grow until they curled.

Sergiu Klainerman explains that the Fields is nothing like the Nobel at all:

Concerning the first issue, the differences between the Fields Medal and the Nobel Prize can hardly be exaggerated. Whatever the original intentions, the Fields Medal is given only to young mathematicians below the age of forty. To have a chance at the medal a mathematician must not only make a major contribution early on, he/she must also be lucky enough to have its importance broadly recognized before the arbitrary fortieth mark. This means that, if an area of mathematics is not represented in the composition of the Fields committee at a given International Congress, truly original and important contributions in that area have very little chance.

In contrast, the Nobel Prize has no age limits. The role of a Nobel committee (in natural sciences) is, at least in principle, to identify those breakthroughs deemed most important by a broad segment of the scientific community and then decide who are the most deserving contributors to it. In contrast with the Fields Medal, which is given strictly to an individual, independent of whether other people might have contributed important ideas to the cited works, the Nobel Prize can be shared by up to three individuals. Thus, in theory, a Nobel Prize is awarded primarily for supreme achievements, and only secondarily to specific individuals. ...

In fact mathematics does not have any prize comparable with the Nobel Prize. The other major prizes — Abel, Shaw, and Wolf — don’t have any age limitation but are almost always given to individuals, based on works done throughout their careers, rather than for specific achievements. Even when the prize is shared there is, in most cases, no identifiable connection between the recipients.

The Abel Prize is maybe the closest to being a Nobel Prize for Math.

There is a wide perception that all the good math is done by young math prodigies. The most famous big math problems of the last 25 years were Fermat's Last Theorem and the Poincare-Thurston conjecture. Both were by mathematicians around age 40, and that is probably the age of highest productivity.

Thursday, July 23, 2015

This year is celebrated as the centenary of general relativity, as ten years ago was the centenary of special relativity. What is the difference? Special relativity is the theory of flat spacetime, including Lorentz transformations and electromagnetism. General relativity is the theory of curved spacetime, and gravity.

Einstein fans disagree over which is the greater accomplishment. Special relativity changed thinking about space and time in a way that permeates XX century physics. General relativity is always lauded as a great theory, but its effects are barely measurable and it has had almost no influence on other branches of physics. It has some influence on cosmology, but not much.

So special relativity is the more influential theory, by far. But some Einstein fans prefer to praise general relativity, because that was a conceptually much more difficult accomplishment. Special relativity can be easily explained with some undergraduate linear algebra, but general relativity requires tensors and differential geometry.

Einstein's role was also different. His 1905 special relativity paper was written on his own, building on published papers. His 1915 general relativity was a collaboration with mathematicians. Some people see one as more credit-worthy than the other.

Sometimes people say that special relativity is just about constant velocity inertial motion, but that is not how it was viewed in the early days, say 1895-1910. It was often applied to accelerating electrons and other particles. Gravitational time dilation can be calculated by comparing to acceleration in a flat spacetime. Viewed this way, the only truly measurable general relativity effects are things like precession of Mercury's orbit, and that is a very tiny effect that took centuries to notice.

Even if relativity had never been discovered, we would probably still have GPS. Nobody would understand why the satellite clocks had to be re-synchronized so often, but they could have figured out some heuristics for resetting the clocks.

Julia Galef: You mentioned the concept of simplicity. I've encountered a lot of
confusion -- also experienced a lot of confusion – over, how do you decide which theory is simpler than another theory?

For example, I've heard critiques of the Many Worlds, or Everett, interpretation of quantum mechanics, to the effect that, "Look, if you're going posit this infinite or uncountably large number of worlds in order to explain this data we're getting, then that's an incredibly extravagant, or incredibly complex, theory. And we should really go for a simpler one, in which there is only one world MM the world that we can see, basically."

Sean Carroll: I would say there are various reasonable critiques of the Many Worlds program; that is not one of them.

Julia Galef: Right. That's what I thought you'd say. [00:14:00]

Sean Carroll: Yeah. To put it as bluntly as possible, that's just wrong. That's just a mistake. It's just a misunderstanding.

Because, again, we're not positing many, many worlds. We are taking the formalism of quantum mechanics that is always there. The Hilbert space, that we call it, which is where the wave function lives, it’s the mathematical structure that a particular quantum state is an element of. The Hilbert space is just as big for someone doing a different interpretation as for someone doing Many Worlds. It doesn't get any bigger. Hilbert space is big. It includes a lot of possibilities. All we're saying is, Hilbert space is all there is, then you stop after you have that. There’s not other structures or other rules or other interpretative dances that you're allowed to do.

To say that positing a lot of worlds is extravagant is to get it exactly backwards. We're positing the minimal mathematical structure needed to make sense of quantum mechanics. Everyone posits Hilbert space. We're just admitting that it's real rather than denying that.

No, Carroll misunderstands math and physics.

Probability is a mathematical device for estimating the likelihood of an event occurring. Carroll says that quantum mechanics is all about probability, but he rejects the way everyone else understands probability. To him, all events occur with certainty, but maybe in other universes.

Physics is about observables. But Carroll insists on attributing reality to all these extra universes that no one can ever observe.

I have posted more detailed arguments on what is wrong with many-worlds. I just want to note here that the blind is leading the blind.

The conversation gets goofier when they discuss morality.

Julia Galef: Right. There was this case -- I don't remember who this was -- one Everettian who I know, she was crossing the street and I guess she wasn't looking where she was going, and the car slammed on its brakes to avoid hitting her.

She was really shaken by this -- which that made sense to me, It makes sense to be shaken if you're almost hit by a car -- but she then explains that the reason she felt so shaken was that she had "lost a lot of measure." In other words, there were a lot of almost identical copies of her who had gotten hit by the car, since it was kind of a toss up whether the car would have hit her or not. Over the set of all copies of her --

Sean Carroll: I'm not sure that attitude can be consistently maintained if you also believe in a block universe version of time, where eventually we're all dead.

Julia Galef: I'll past that on! I don't know if that will cheer her up or not.

This is crazy talk. No, that Everettian did not lose copies of herself in alternate universes. The block universe version of time is another stupid idea, and has little to do with the situation.

Thursday, July 16, 2015

FitzGerald and Lorentz first derived, independently, the length contraction as a logical consequence of the Michelson-Morley experiment showing a constant speed of light. Then Lorentz developed a more sophisticated theory where the contraction is also explained by electromagnetism pulling atoms closer together. Einstein later called former a principle theory, and the latter a constructive theory.

I show that Albert Einstein’s distinction between principle and constructive theories was predated by Hendrik A. Lorentz’s equivalent distinction between mechanism- and principle-theories. I further argue that Lorentz’s views toward realism similarly prefigure what Arthur Fine identified as Einstein’s ‘‘motivational realism.’’

Many discussion of crediting Einstein for relativity are based on Einstein avoiding the constructive theory in his 1905 paper, and sticking to the principle-theory approach that Lorentz had earlier.

Frisch's paper further shows that Einstein's views on relativity were pretty much the same as Lorentz's.

Monday, July 13, 2015

While we know how the science turned out, people like Bellarmine and the majority of astronomers did not have the benefit of our hindsight. At the time the question was far from settled and there were actually no less than seven competing models under debate, of which the Copernican model was very much the unfavoured outsider. They consisted of:

So the issue was not just heliocentrism v geocentrism, or whether the Earth moves. There were a bunch of possibilities, and it was not clear how to physically distinguish them.

He says "we know how the science turned out", as if everyone knows that Kepler turned out to be right. Kepler's model did give the best results for a century or so. Then can Newtonian models with planets like Jupiter pulling other planets out of their elliptical orbits. For the last century, the consensus has been general relativity, where motion is relative and you can think of the Earth as stationary or as moving however you please, as long as the coordinate transformations are done properly in the covariant equations.

I suspected that the trillion odors were bogus, because it seems unlikely and because it is hard to see how a test could confirm it.

Comparing to colors, I can easily imagine showing someone a bunch of random colors, confirming that he can distinguish them, and deducing that trillions of colors are distinguishable. Likewise with musical sounds. But if the data passes thru some low dimensional filter, then there will be trillions of different inputs that are perceived as identical. Unless the experiment is set up to produce these examples, they will be missed.

I did not read the papers, but it is amusing how such a completely bogus result can be reported in the most prestigious science journals, and widely reported as fact in the popular press.